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Metamath Proof Explorer

Theorem nfcxfr

Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by Mario Carneiro, 11-Aug-2016)

Ref Expression
Hypotheses nfcxfr.1 ⊢ A = B
nfcxfr.2 ⊢ Ⅎ _ x B
Assertion nfcxfr ⊢ Ⅎ _ x A

Proof

Step Hyp Ref Expression
1 nfcxfr.1 ⊢ A = B
2 nfcxfr.2 ⊢ Ⅎ _ x B
3 1 nfceqi ⊢ Ⅎ _ x A ↔ Ⅎ _ x B
4 2 3 mpbir ⊢ Ⅎ _ x A